Photonic crystals are a class of man-made materials, which are often referred to as “meta-materials.” Photonic crystals are formed by dispersing a material of one dielectric constant periodically within a matrix having a different dielectric constant. A one-dimensional photonic crystal is a three-dimensional structure that exhibits periodicity in dielectric constant in only one dimension. Bragg mirrors are an example of a one-dimensional photonic crystal. The alternating thin layers have different dielectric constants and refractive indices. The combination of several thin layers forms a three-dimensional structure that exhibits periodicity in dielectric constant in only the direction orthogonal to the planes of the thin layers. No periodicity is exhibited in either of the two dimensions contained within the plane of the layers.
A two-dimensional (2D) photonic crystal can be formed by periodically dispersing rods or columns of a material of one dielectric constant within a matrix having a different dielectric constant. 2D photonic crystals exhibit periodicity in two dimensions (i.e., the directions perpendicular to the length of the rods or columns) but no periodicity is exhibited in the direction parallel to the length of the columns.
Finally, a three-dimensional photonic crystal can be formed by periodically dispersing small spheres or other spatially confined areas of a first material having a first dielectric constant within a matrix of a second material having a second, different, dielectric constant. Three-dimensional photonic crystals exhibit periodicity in dielectric constant in all three dimensions within the crystal.
Photonic crystals may exhibit a photonic bandgap over a range of frequencies in directions exhibiting periodicity in dielectric constant. In other words, there may be a range of frequencies of electromagnetic radiation that will not be transmitted through the photonic crystal in the directions exhibiting dielectric periodicity. This range of frequencies that are not transmitted is known as a photonic bandgap of the photonic crystal.
For an introduction to photonic crystals and their uses and applications, the reader is referred to John D. Joannopoulos, Robert D. Meade & Joshua N. Winn, Photonic Crystals—Molding the Flow of Light, (Princeton University Press 1995) and K. Inoue & K. Ithaca, Photonic Crystals—Physics, Fabrication and Applications, (Springer 2004)
In natural materials, electromagnetic radiation is refracted at a specific angle and in a specific direction when it encounters a junction between two materials. A class of meta-materials has been studied that refract electromagnetic radiation in the opposite direction from the direction of natural materials. These materials exhibiting negative refraction are often called super-lenses for their ability to produce images with sub-wavelength resolution. Recently, it has been shown that photonic crystals may exhibit this negative refractive index. Many new and useful applications may be possible for these super-lens structures, particularly photonic crystals exhibiting negative refraction.